Today I want to talk about graphical representations. Specifically, I want to discuss some of the graph types that I’ve been teaching to my students in “Speaking with Numbers: Effective Use of Statistics”. Feel free to contact me if you want more details on the course - I’m happy to send you the info!

For this course I am requiring the students to complete the lesson before our course meeting in order to spend the actual class time on DOING the data collection, graph creation, and analysis process. What follows is part of the lesson itself.

**Graph Types: histogram, stem & leaf plot, and pie chart**

This lesson will introduce three graph types: the frequency histogram, the stem & leaf plot, and the pie chart (also sometimes referred to as a circle graph).

- Histograms come in two types: frequency and relative frequency. They are a type of bar graph in which the bars touch and the vertical axis shows how often something occurs. They can only display quantitative data and will display either class boundaries or class midpoints along with frequency or relative frequency. They require creating a tally chart. We can create histograms using our TI83+. We will focus on the frequency histogram type.
- Stem-and-leaf plots are similar to histograms in that they can show trends in the data set; however, they have an advantage: they show individual data values. They can only display quantitative data and the data set must have at least two digits. Additionally, stem and leaf plots can only represent one variable (e.g. height) so they cannot be used to compare variables or to illustrate correlation. They are easy to create by hand.
- Pie graphs are different from the other two discussed here for two reasons: they can illustrate qualitative data along with quantitative data and they allow comparisons to be made (“parts” to the “whole”). Each sector of the circle is proportional to the value being displayed. They are tedious to create by hand (require special tools: ruler, compass, & protractor) but we can create them using Excel.

This is a class I’m teaching online so I included a comments section asking students to participate:

Using the comments tool below, give one real life example you can think of that could be represented with each graph type. Please don't use examples already given in the lesson.

Here are some of their responses:

In the lesson itself, I gave information about each graph type, showed examples, and asked questions to ensure understanding. For example, here is part of the lesson on Stem & Leaf graphs:

In the stem and leaf plot (also known as a stem and leaf diagram) shown above, you see some of the "best practices" for representing data graphically. First, the graph has a descriptive title (in this case, it is clear that this data is representing the number of sit-ups completed). Second, it has a key (also known as a legend) to help readers who might be unfamiliar with this graph type know how to read it.

As a teacher, this image is a good one because it also labels how this graph type gets its name. As we can see, the "stem" is the larger digit (in this case, tens) and the "leaves" is the smaller digit (in this case, ones).

The total number of leaves tells you the sample size of the data (usually represented by the variable n). It is also worth noting that every single piece of data is represented (shown) with this graph type -- for example, we can see that two people were able to do 50 sit-ups because there are two 0 leaves next to the 5 stem. That means that the mode (the data value that occurs the most) is able to be determined with a stem-and-leaf plot.

In the lesson, I also asked questions like the following (based on the graph shown above):

Even though the questions were relatively simple and the online platform for hosting the lesson material was fairly basic, all students reported that they enjoyed the way it was presented and felt it was engaging. It is also worth noting that there was 100% participation of the students with the lesson prior to the live class session.

During our live class session, students were asked to complete an activity sheet. The format I use when I create an activity sheet is similar to the 3-act math lessons by Dan Meyer in that there are three parts to it. For mine, I have a pre-class part (completed by the student individually before the activity), an in-class part (competed collectively by the class during the activity), and a reflection part (completed individually or in small groups after the completion of the activity).

As always, I'd love to hear from you. Especially, I would love to hear if you have additional ideas for effective use of statistics, creative ways to teach accurately representing data with graphs, suggestions for how to communicate with numbers, or other comments about this blog post!

**References:**

LINK for the Create a Graph tool by NCES

LINK for Plotly, the graphing library for Python

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**The Solver Blog**

**Author: ****Dr. Diana S. Perdue**